Please answer all

1) Suppose you and a colleague collect a data set. You use the data to form a 90% confidence interval for the sample mean, and your college forms a 95% confidence interval. Which interval is larger?

A. 95% confidence interval

B. 90% confidence interval

C. We do not have enough information to answer this question

D. Both intervals have the same width

2) Please consider the value of Prob(X > 2). Is this probability value larger if X is standard normal or if X has a t-distribution with 5 degrees of freedom?

A. Larger for X with standard normal distribution

B. Probability value will be the same for both distributions

C. Larger for X with t-distribution

D. We do not have enough information to answer this question

3) In general, the probability of a Type I error is inversely proportional to the probability of a Type II error. What happens to the Type II error probability if we change alpha from 5% to 10%?

A. Type II error probability increases

B. We do not have enough information to answer this question

C. Type II error rate remains unchanged

D. Type II error probability declines

4) For a sample of size n=25, which confidence interval for the sample mean is more conservative (narrower), an interval based on the t-distribution or the standard normal distribution?

A. We do not have enough information to answer this question

B. Confidence interval based on the standard normal distribution

C. Both intervals have the same width

D. Confidence interval based on the t-distribution

5) Suppose X is a standard normal random variable. What can we say about Prob(X > 3) compared to Prob(X < -3)?

A. Prob (X > 3) is larger

B. These probability values are equal

C. We do not have enough information to answer this question

D. Prob (X < -3) is larger

6) Suppose we collect more data so the sample size (n) increases but the sample mean and standard deviation do not change. What happens to the boundaries of the confidence interval for the mean based on the standard normal distribution?

A. Boundaries may widen or narrows under these circumstances

B. Boundaries become narrower

C. Boundaries do not change

D. Boundaries become wider